NAME¶

SPTRFS - improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and tridiagonal, and provides error bounds and backward error estimates for the solution

SYNOPSIS¶

SUBROUTINE SPTRFS(

N, NRHS, D, E, DF, EF, B, LDB, X, LDX, FERR, BERR, WORK, INFO )

INTEGER INFO, LDB, LDX, N, NRHS REAL B( LDB, * ), BERR( * ), D( * ), DF( * ), E( * ), EF( * ), FERR( * ), WORK( * ), X( LDX, * )

PURPOSE¶

SPTRFS improves the computed solution to a system of linear equations when the coefficient matrix is symmetric positive definite and tridiagonal, and provides error bounds and backward error estimates for the solution.

ARGUMENTS¶

N (input) INTEGER

The order of the matrix A. N >= 0.

NRHS (input) INTEGER

The number of right hand sides, i.e., the number of columns of the matrix B. NRHS >= 0.

D (input) REAL array, dimension (N)

The n diagonal elements of the tridiagonal matrix A.

E (input) REAL array, dimension (N-1)

The (n-1) subdiagonal elements of the tridiagonal matrix A.

DF (input) REAL array, dimension (N)

The n diagonal elements of the diagonal matrix D from the factorization computed by SPTTRF.

EF (input) REAL array, dimension (N-1)

The (n-1) subdiagonal elements of the unit bidiagonal factor L from the factorization computed by SPTTRF.

B (input) REAL array, dimension (LDB,NRHS)

The right hand side matrix B.

LDB (input) INTEGER

The leading dimension of the array B. LDB >= max(1,N).

X (input/output) REAL array, dimension (LDX,NRHS)

On entry, the solution matrix X, as computed by SPTTRS. On exit, the improved solution matrix X.

LDX (input) INTEGER

The leading dimension of the array X. LDX >= max(1,N).

FERR (output) REAL array, dimension (NRHS)

The forward error bound for each solution vector X(j) (the j-th column of the solution matrix X). If XTRUE is the true solution corresponding to X(j), FERR(j) is an estimated upper bound for the magnitude of the largest element in (X(j) - XTRUE) divided by the magnitude of the largest element in X(j).

BERR (output) REAL array, dimension (NRHS)

The componentwise relative backward error of each solution vector X(j) (i.e., the smallest relative change in any element of A or B that makes X(j) an exact solution).

WORK (workspace) REAL array, dimension (2*N)

INFO (output) INTEGER

= 0: successful exit
< 0: if INFO = -i, the i-th argument had an illegal value

PARAMETERS¶

ITMAX is the maximum number of steps of iterative refinement.